A study by the lattice discrete element method for exploring the fractal nature of scale effects

Nowadays, there are many applications in the field of Engineering related to quasi-brittle materials such as ceramics, natural stones, and concrete, among others. When damage is produced, two phenomena can take place: the damage produced governs the collapse process when working with this type of material, and its random nature rules the nonlinear behavior up to the collapse. The interaction among clouds of micro-cracks generates the localization process that implies transforming a continuum domain into a discontinue one. This process also governs the size effect, that is, the changes of the global parameters as the strength and characteristic strain and energies when the size of the structure changes. Some aspects of the scaling law based on the fractal concepts proposed by Prof Carpinteri are analyzed in this work. On the other hand, the Discrete Method is an interesting option to be used in the simulation collapse process of quasi-brittle materials. This method can allow failures with relative ease. Moreover, it can also help to relax the continuum hypothesis. In the present work, a version of the Discrete Element Method is used to simulate the mechanical behavior of different size specimens until collapse by analyzing the size effect represented by this method. This work presents two sets of examples. Its results allow the researchers to see the connection between the numerical results regarding the size effect and the theoretical law based on the fractal dimension of the parameter studied. Two main aspects appear as a result of the analysis presented here. Understand better some aspects of the size effect using the numerical tool and show that the Lattice Discrete Element Method has enough robustness to be applied in the nonlinear analysis of structures built by quasi-brittle materials

Applications of lattice method in the simulation of crack path in heterogeneous materials

The simulation of critical and subcritical crack propagation in heterogeneous materials is not a simpleproblem in computational mechanics. These topics can be studied with different theoretical tools. In the crackpropagation problem it is necessary to lead on the interface between the continuum and the discontinuity, andthis region has different characteristics when we change the scale level point of view. In this context, this workapplies a version of the lattice discrete element method (LDEM) in the study of such matters. This approach letsus to discretize the continuum with a regular tridimensional truss where the elements have an equivalent stiffnessconsistent with the material one wishes to model. The masses are lumped in the nodes and an uni-axial bilinearrelation, inspired in the Hilleborg constitutive law, is assumed for the elements. The random characteristics of thematerial are introduced in the model considering the material toughness as a random field with defined statisticalproperties. It is important to highlight that the energy balance consistence is maintained during all the process.The spatial discretization lets us arrive to a motion equation that can be solved using an explicit scheme ofintegration on time. Two examples are shown in the present paper; one of them illustrates the possibilities of thismethod in simulating critical crack propagation in a solid mechanics problem: a simple geometry of grade material.In the second example, a simulation of subcritical crack growth is presented, when a pre-fissured quasi-brittlebody is submitted to cyclic loading. In this second example, a strategy to measure crack advance in the model isproposed. Finally, obtained results and the performance of the model are discussed

Long-Range Correlations and Natural Time Series Analyses from Acoustic Emission Signals

This work focuses on analyzing acoustic emission (AE) signals as a means to predict failure in structures. There are two main approaches that are considered: (i) long-range correlation analysis using both the Hurst (H) and the detrended fluctuation analysis (DFA) exponents, and (ii) natural time domain (NT) analysis. These methodologies are applied to the data that were collected from two application examples: a glass fiber-reinforced polymeric plate and a spaghetti bridge model, where both structures were subjected to increasing loads until collapse. A traditional (AE) signal analysis was also performed to reference the study of the other methods. The results indicate that the proposed methods yield reliable indication of failure in the studied structures

Applications of lattice method in the simulation of crack path in heterogeneous materials

The simulation of critical and subcritical crack propagation in heterogeneous materials is not a simple problem in computational mechanics. These topics can be studied with different theoretical tools. In the crack propagation problem it is necessary to lead on the interface between the continuum and the discontinuity, and this region has different characteristics when we change the scale level point of view. In this context, this work applies a version of the lattice discrete element method (LDEM) in the study of such matters. This approach lets us to discretize the continuum with a regular tridimensional truss where the elements have an equivalent stiffness consistent with the material one wishes to model. The masses are lumped in the nodes and an uni-axial bilinear relation, inspired in the Hilleborg constitutive law, is assumed for the elements. The random characteristics of the material are introduced in the model considering the material toughness as a random field with defined statistical properties. It is important to highlight that the energy balance consistence is maintained during all the process. The spatial discretization lets us arrive to a motion equation that can be solved using an explicit scheme of integration on time. Two examples are shown in the present paper; one of them illustrates the possibilities of this method in simulating critical crack propagation in a solid mechanics problem: a simple geometry of grade material. In the second example, a simulation of subcritical crack growth is presented, when a pre-fissured quasi-brittle body is submitted to cyclic loading. In this second example, a strategy to measure crack advance in the model is proposed. Finally, obtained results and the performance of the model are discussed

Size effect in heterogeneous materials analyzed through a lattice discrete element method approach

In the Lattice Discrete Element Method (LDEM), different types of mass are considered to be lumped at nodal points and linked by means of one-dimensional elements with arbitrary constitutive relations. In previous studies on the tensile fracture behavior of rock samples, it was verified that numerical predictions of fracture of non-homogeneous materials using LDEM models are feasible and yield results that are consistent with the experimental evidence available so far. In the present paper, a discussion of the results obtained with the LDEM is presented. A set of rock specimens of different sizes, subjected to monotonically increasing simple tensions, are simulated with LDEM. The results were analyzed from the perspective of the brittleness number, proposed by Alberto Carpinteri, to measure the brittleness level of the structure under study. The satisfactory correlation between the experimental results and LDEM results confirms the robustness of this method as a numerical tool to model fracture processes in quasi-brittle materials

The first fully characterized 1,3-polyazulene: High electrical conductivity resulting from cation radicals and polycations generated upon protonation

10.1021/ol0274615Organic Letters57995-99